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Evaluate int(sec^(2)x dx)/(sqrt(2+3tan^(...

Evaluate `int(sec^(2)x dx)/(sqrt(2+3tan^(2)x)).`

Text Solution

Verified by Experts

`int(tanx dx)/(sqrt(2+3tan^(2)x))=int(sinx dx)/(sqrt(2cos^(2)x+3sin^(2)x))`
`=int(sinx dx)/(sqrt(2cos^(2)x+3(1-cos^(2)x)))`
`=int(sinx dx)/(sqrt(3-cos^(2)x))`
`=-int(dt)/(sqrt(3-t^(2)))`
`=-"sin"^(-1)(t)/(sqrt(3))+c`
`=-"sin"^(-1)(cosx)/(sqrt(3))+c`
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